#
# Involute gear tooth generator
#
# agm/NYCR, 2008
#

# curves or line segments?
# working angle is expressed in degrees rather than radians...
# is that wise?

from math import *
import rep
from writeDxf import writeToDxf

# involute conv. functions
def involuteLength(alpha):
    "Length of involute of unit circle with given alpha"
    return sqrt((alpha**2)+1)

def involuteAngle(alpha):
    "Angle of involute of unit circle at given alpha"
    return abs(alpha-atan(alpha))

class InvoluteGear:
    def __init__(self,module,teeth,addendum=None,working_angle=20.0,clearance=None):
        if not addendum:
            addendum=module
        if not clearance:
            clearance=addendum/8.0
        self.module=module
        self.teeth=teeth
        self.addendum=addendum
        self.wa=radians(working_angle)
        self.clearance=clearance
        # calculate radii
        self.r_pitch=module*teeth/2.0
        self.r_base=self.r_pitch/involuteLength(self.wa)
        self.r_addendum=self.r_pitch+addendum
        self.r_clearance=self.r_pitch-(addendum+clearance)
        # tooth width
        self.tooth_width_subtends=pi/teeth
        # angle at involute intersection with pitch circle (relative to base)
        self.angle_pitch=involuteAngle(self.wa)
        # angle at involute intersection with addendum circle (relative to base)
        self.alpha_addendum=sqrt(((self.r_addendum/self.r_base)**2)-1)
        self.angle_addendum=involuteAngle(self.alpha_addendum)

    def drawTeeth(self,path,subdiv=20):
        theta = 2.0*pi/self.teeth
        for i in range(self.teeth):
            path.rotate(rep.Path.Point(0,0),theta)
            self.drawTooth(path,subdiv)

    def drawTooth(self,path,subdiv=20):
        # rising edge of tooth
        rising_angle=(self.tooth_width_subtends/2.0)+self.angle_pitch
        path.startAt(rep.Path.Polar(self.r_clearance,rising_angle))
        for alpha in [x*self.alpha_addendum/subdiv for x in range(subdiv+1)]:
            path.lineTo(rep.Path.Polar(involuteLength(alpha)*self.r_base,
                                       rising_angle-involuteAngle(alpha)))
        # top of tooth
        top_angle=rising_angle-self.angle_addendum
        arc = rep.Path.Arc(rep.Path.Point(0,0),self.r_addendum,-top_angle,top_angle)
        path.appendArc(arc)
        # falling end of tooth
        path.startAt(rep.Path.Polar(self.r_addendum,-top_angle))
        for alpha in [x*self.alpha_addendum/subdiv for x in range(subdiv-1,-1,-1)]:
            path.lineTo(rep.Path.Polar(involuteLength(alpha)*self.r_base,
                                       -rising_angle+involuteAngle(alpha)))
        path.lineTo(rep.Path.Polar(self.r_clearance,-rising_angle))
        # bottom of tooth
        arc = rep.Path.Arc(rep.Path.Point(0,0),self.r_clearance,rising_angle-2*self.tooth_width_subtends,-rising_angle)
        path.appendArc(arc)
        

if __name__ == '__main__':
    print("ten teeth")
    gear=InvoluteGear(10,80)
    path = rep.Path()
    gear.drawTeeth(path)
    writeToDxf("80.dxf",path)